In the physics of relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s2 being a standard reference of gravitational acceleration at the Earth's surface) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus:
Einstein also referred to two reference frames, K and K'. K is a uniform gravitational field, whereas K' has no gravitational field but is uniformly accelerated such that objects in the two frames experience identical forces:
This observation was the start of a process that culminated in general relativity. Einstein suggested that it should be elevated to the status of a general principle when constructing his theory of relativity:
Einstein combined the equivalence principle with special relativity to predict that clocks run at different rates in a gravitational potential, and light rays bend in a gravitational field, even before he developed the concept of curved spacetime.
So the original equivalence principle, as described by Einstein, concluded that free-fall and inertial motion were physically equivalent. This form of the equivalence principle can be stated as follows. An observer in a windowless room cannot distinguish between being on the surface of the Earth, and being in a spaceship in deep space accelerating at 1g. This is not strictly true, because massive bodies give rise to tidal effects (caused by variations in the strength and direction of the gravitational field) which are absent from an accelerating spaceship in deep space.
Although the equivalence principle guided the development of general relativity, it is not a founding principle of relativity but rather a simple consequence of the geometrical nature of the theory. In general relativity, objects in free-fall follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doing so.
The weak equivalence principle, also known as the universality of free fall:
Since Einstein developed general relativity, there was a need to develop a framework to test the theory against other possible theories of gravity compatible with special relativity. This was developed by Robert Dicke as part of his program to test general relativity. Two new principles were suggested, the so-called Einstein equivalence principle and the strong equivalence principle, each of which assumes the weak equivalence principle as a starting point. They only differ in whether or not they apply to gravitational experiments.
The Einstein equivalence principle states that the result of a local non-gravitational experiment in an inertial frame of reference is independent of the velocity or location in the universe of the experiment. This is a kind of Copernican extension of Einstein's original formulation, which requires that suitable frames of reference all over the universe behave identically. It is an extension of the postulates of special relativity in that it requires that dimensionless physical values such as the fine-structure constant and electron-to-proton mass ratio be constant. Many physicists believe that any Lorentz invariant theory that satisfies the weak equivalence principle also satisfies the Einstein equivalence principle.
The strong equivalence principle states that the results of any local experiment, gravitational or not, in an inertial frame of reference are independent of where and when in the universe it is conducted. This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which have substantial internal gravitational interactions. It requires that the gravitational constant be the same everywhere in the universe and is incompatible with a fifth force. It is much more restrictive than the Einstein equivalence principle. General relativity is the only known theory of gravity compatible with this form of the equivalence principle.
|John Philoponus||6th Century||Described correctly the effect of dropping balls of different masses||no detectable difference|
|Simon Stevin||~1586||Dropped lead balls of different masses off the Delft churchtower||no detectable difference|
|Galileo Galilei||~1610||Rolling balls down inclined planes||no detectable difference|
|Isaac Newton||~1680||measure the period of pendulums of different mass but identical length||no measurable difference|
|Friedrich Wilhelm Bessel||1832||measure the period of pendulums of different mass but identical length||no measurable difference|
|Loránd Eötvös||1908||measure the torsion on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotation of the Earth||difference is less than 1 part in a billion|
|Roll, Krotkov and Dicke||1964||Torsion balance experiment, dropping aluminum and gold test masses||difference is less than one part in one hundred billion|
|David Scott||1971||Dropped a falcon feather and a hammer at the same time on the Moon||no detectable difference (not a rigorous experiment, but very dramatic being the first lunar one)|
|Braginsky and Panov||1971||Torsion balance, aluminum and platinum test masses, measuring acceleration towards the sun||difference is less than 1 part in a trillion (most accurate to date)|
|Eöt-Wash||1987–||Torsion balance, measuring acceleration of different masses towards the earth, sun and galactic center, using several different kinds of masses||difference is less than a few parts in a trillion|
Experiments are still being performed at the University of Washington which have placed limits on the differential acceleration of objects towards the Earth, the sun and towards dark matter in the galactic center. Future satellite experiments – STEP (Satellite Test of the Equivalence Principle), Galileo Galilei, and MICROSCOPE (MICROSatellite pour l'Observation de Principe d'Equivalence) – will test the weak equivalence principle in space, to much higher accuracy.
The need to continue testing Einstein's theory of gravity may seem superfluous, as it is by far the most elegant theory of gravity known, and is compatible with almost all observations to date (except for instance the Pioneer anomaly). However, no quantum theory of gravity is known, and most suggestions violate one of the equivalence principles at some level. String theory, supergravity and even quintessence, for example, seem to violate the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths. These fields should generate fifth forces and variation of the fundamental constants. There are a number of mechanisms that have been suggested by physicists to reduce these violations of the equivalence principle to below observable levels.
Laboratory equivalence principle composition and spin tests are supported by observation of binary pulsar PSR J0737-3039 (arXiv, Matters of Gravity). A neutron star core might be strange matter, pion condensate, lambda hyperon, delta isobar, or free quark matter. Extreme bound (gravitational binding energy ~30% of disassembled rest mass), spinning (~20% of lightspeed at equator), magnetic (~108 tesla), dense (4-9x1014 g/cm3), superconducting neutronium obeys general relativity orbital predictions within 0.05% or better.
The equivalence principle is untested against opposite geometric parity (chirality in all directions) mass distributions. A parity Eötvös experiment contrasting solid single crystal spheres of identical composition α-quartz in enantiomorphic space groups P3121 (right-handed screw axis) versus P3221 (left-handed screw axis) is appropriate. Equivalence principle parity violation validates a chiral vacuum background forbidden within general relativity but allowed within Einstein-Cartan theory; affine, teleparallel, and noncomutative gravitation theories.
The principle of relativity implies that the outcome of local experiments must be independent of the velocity of the apparatus, so the most important consequence of this principle is the Copernican idea that any of the fundamental physical parameters – other than masses and Newton's gravitational constant – must not depend on where in space or time we measure them. In practice, these are dimensionless numbers, such as the ratio of two masses, or coupling constants such as the fine-structure constant.
Schiff's conjecture suggests that the weak equivalence principle actually implies the Einstein equivalence principle, but it has not been proven. Nonetheless, the two principles are tested with very different kinds of experiments. The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley and Durand).
|Constant||Year||Method||Limit on fractional change|
|fine structure constant||1976||Oklo||10-7|
|weak interaction constant||1976||Oklo||10-2|
|electron-proton mass ratio||2002||quasars||10-4|
|proton gyromagnetic factor||1976||astrophysical||10-1|
There have been a number of controversial attempts to constrain the variation of the strong interaction constant. There have been several suggestions that "constants" do vary on cosmological scales. The best known is the reported detection of variation (at the 10-5 level) of the fine-structure constant from measurements of distant quasars, see Webb et al. Other researchers dispute these findings. Other tests of the Einstein equivalence principle are gravitational redshift experiments, such as the Pound-Rebka experiment which test the position independence of experiments.
The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe. Einstein's theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans-Dicke theory, satisfy only the Einstein equivalence principle.
Thus, the strong equivalence principle can be tested by searching for fifth forces (deviations from the gravitational force-law predicted by general relativity). These experiments typically look for failures of the inverse-square law (specifically Yukawa forces or failures of Birkhoff's theorem) behavior of gravity in the laboratory. The most accurate tests over short distances have been performed by the Eöt-Wash group. A future satellite experiment, SEE (Satellite Energy Exchange), will search for fifth forces in space and should be able to further constrain violations of the strong equivalence principle. Other limits, looking for much longer-range forces, have been placed by searching for the Nordtvedt effect, a "polarization" of solar system orbits that would be caused by gravitational self-energy accelerating at a different rate from normal matter. This effect has been sensitively tested by the Lunar Laser Ranging Experiment. Other tests include studying the deflection of radiation from distant radio sources by the sun, which can be accurately measured by very long baseline interferometry. Another sensitive test comes from measurements of the frequency shift of signals to and from the Cassini spacecraft. Together, these measurements have put tight limits on Brans-Dicke theory and other alternative theories of gravity.